Sums of hermitian squares and the BMV conjecture

Recently Lieb and Seiringer showed that the Bessis-Moussa-Villani conjecture from quantum physics can be restated in the following purely algebraic way: The sum of all words in two positive semidefinite matrices where the number of each of the two letters is fixed is always a matrix with nonnegative trace. We show that this statement holds if the words are of length at most 13. This has previously been known only up to length 7. In our proof, we establish a connection to sums of hermitian squares of polynomials in noncommuting variables and to semidefinite programming. As a by-product we obtain an example of a real polynomial in two noncommuting variables having nonnegative trace on all symmetric matrices of the same size, yet not being a sum of hermitian squares and commutators.Comment: 21 pages; minor changes; a companion Mathematica notebook is now available in the source fil

Strong duality in conic linear programming: facial reduction and extended duals

The facial reduction algorithm of Borwein and Wolkowicz and the extended dual of Ramana provide a strong dual for the conic linear program $$(P) \sup {<c, x> | Ax \leq_K b}$$ in the absence of any constraint qualification. The facial reduction algorithm solves a sequence of auxiliary optimization problems to obtain such a dual. Ramana's dual is applicable when (P) is a semidefinite program (SDP) and is an explicit SDP itself. Ramana, Tuncel, and Wolkowicz showed that these approaches are closely related; in particular, they proved the correctness of Ramana's dual using certificates from a facial reduction algorithm. Here we give a clear and self-contained exposition of facial reduction, of extended duals, and generalize Ramana's dual: -- we state a simple facial reduction algorithm and prove its correctness; and -- building on this algorithm we construct a family of extended duals when $K$ is a {\em nice} cone. This class of cones includes the semidefinite cone and other important cones.Comment: A previous version of this paper appeared as "A simple derivation of a facial reduction algorithm and extended dual systems", technical report, Columbia University, 2000, available from http://www.unc.edu/~pataki/papers/fr.pdf Jonfest, a conference in honor of Jonathan Borwein's 60th birthday, 201

Inter- and intragrain currents in bulk melt-grown YBaCuO rings

A simple contactless method suitable to discern between the intergrain (circular) current, which flows in the thin superconducting ring, and the intragrain current, which does not cross the weakest link, has been proposed. At first, we show that the intergrain current may directly be estimated from the magnetic flux density $B(\pm z_0)$ measured by the Hall sensor positioned in the special points $\pm z_0$ above/below the ring center. The experimental and the numerical techniques to determine the value $z_0$ are discussed. Being very promising for characterization of a current flowing across the joints in welded YBaCuO rings (its dependencies on the temperature and the external magnetic field as well as the time dissipation), the approach has been applied to study corresponding properties of the intra- and intergrain currents flowing across the $a$-twisted grain boundaries which are frequent in bulk melt-textured YBaCuO samples. We present experimental data related to the flux penetration inside a bore of MT YBaCuO rings both in the non-magnetized, virgin state and during the field reversal. The shielding properties and their dependence on external magnetic fields are also studied. Besides, we consider the flux creep effects and their influence on the current re-distribution during a dwell.Comment: 13 pages, 16 figures (EPS), RevTeX4. In the revised version, corrections to perturbing effects near the weak links are introduced, one more figure is added. lin

Calsequestrin as a risk factor in Graves’ hyperthyroidism and Graves’ ophthalmopathy patients

Background: The pathogenesis of Graves’ ophthalmopathy (GO), Graves’ hyperthyroidism (GH) and the mechanisms for its link to thyroid autoimmunity are poorly understood. Our research focuses on the role of the skeletal muscle calcium binding protein calsequestrin (CASQ1) in thyroid. We measured the concentration of the CASQ1 protein correlating levels with parameters of the eye signs, CASQ1 antibody levels and CASQ1 gene polymorphism rs3838284. Methods: CASQ1 protein was measured by quantitative Western Blotting. The protein concentrations were expressed as pmol/mg total protein by reference to CASQ1 standards. Results: Western blot analysis showed the presence of two forms of CASQ1 in the thyroid. The mean concentration of CASQ1 protein was significantly reduced in patients with Graves’ disease, compared to thyroid from control subjects with multi-nodular goitre or thyroid cancer. Although in patients with GO it was lower than that, compared with patients with GH this difference was not significant. Reduced CASQ1 in Graves’ thyroid correlated with the homozygous genotype of the rs3838284 CASQ1 polymorphism. Conclusions: Decreased CASQ1 in the thyroid of patients with Graves’ disease compared to thyroid from control subjects is not explained but may reflect consumption of the protein during an autoimmune reaction against CASQ1 in the thyroid

NKG2A is a late immune checkpoint on CD8 T cells and marks repeated stimulation and cell division

The surface inhibitory receptor NKG2A forms heterodimers with the invariant CD94 chain and is expressed on a subset of activated CD8 T cells. As antibodies to block NKG2A are currently tested in several efficacy trials for different tumor indications, it is important to characterize the NKG2A(+) CD8 T cell population in the context of other inhibitory receptors. Here we used a well-controlled culture system to study the kinetics of inhibitory receptor expression. Naive mouse CD8 T cells were synchronously and repeatedly activated by artificial antigen presenting cells in the presence of the homeostatic cytokine IL-7. The results revealed NKG2A as a late inhibitory receptor, expressed after repeated cognate antigen stimulations. In contrast, the expression of PD-1, TIGIT and LAG-3 was rapidly induced, hours after first contact and subsequently down regulated during each resting phase. This late, but stable expression kinetics of NKG2A was most similar to that of TIM-3 and CD39. Importantly, single-cell transcriptomics of human tumor-infiltrating lymphocytes (TILs) showed indeed that these receptors were often coexpressed by the same CD8 T cell cluster. Furthermore, NKG2A expression was associated with cell division and was promoted by TGF-beta in vitro, although TGF-beta signaling was not necessary in a mouse tumor model in vivo. In summary, our data show that PD-1 reflects recent TCR triggering, but that NKG2A is induced after repeated antigen stimulations and represents a late inhibitory receptor. Together with TIM-3 and CD39, NKG2A might thus mark actively dividing tumor-specific TILs.Experimental cancer immunology and therap

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

Jet size dependence of single jet suppression in lead-lead collisions at sqrt(s(NN)) = 2.76 TeV with the ATLAS detector at the LHC

Measurements of inclusive jet suppression in heavy ion collisions at the LHC provide direct sensitivity to the physics of jet quenching. In a sample of lead-lead collisions at sqrt(s) = 2.76 TeV corresponding to an integrated luminosity of approximately 7 inverse microbarns, ATLAS has measured jets with a calorimeter over the pseudorapidity interval |eta| < 2.1 and over the transverse momentum range 38 < pT < 210 GeV. Jets were reconstructed using the anti-kt algorithm with values for the distance parameter that determines the nominal jet radius of R = 0.2, 0.3, 0.4 and 0.5. The centrality dependence of the jet yield is characterized by the jet "central-to-peripheral ratio," Rcp. Jet production is found to be suppressed by approximately a factor of two in the 10% most central collisions relative to peripheral collisions. Rcp varies smoothly with centrality as characterized by the number of participating nucleons. The observed suppression is only weakly dependent on jet radius and transverse momentum. These results provide the first direct measurement of inclusive jet suppression in heavy ion collisions and complement previous measurements of dijet transverse energy imbalance at the LHC.Comment: 15 pages plus author list (30 pages total), 8 figures, 2 tables, submitted to Physics Letters B. All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HION-2011-02

Possible discovery of Calvera's supernova remnant

Stars and planetary system

Measurement of event-shape observables in Z→ℓ+ℓ− events in pp collisions at √ s=7 TeV with the ATLAS detector at the LHC

Event-shape observables measured using charged particles in inclusive $Z$-boson events are presented, using the electron and muon decay modes of the $Z$ bosons. The measurements are based on an integrated luminosity of $1.1 {\rm fb}^{-1}$ of proton--proton collisions recorded by the ATLAS detector at the LHC at a centre-of-mass energy $\sqrt{s}=7$ TeV. Charged-particle distributions, excluding the lepton--antilepton pair from the $Z$-boson decay, are measured in different ranges of transverse momentum of the $Z$ boson. Distributions include multiplicity, scalar sum of transverse momenta, beam thrust, transverse thrust, spherocity, and $\mathcal{F}$-parameter, which are in particular sensitive to properties of the underlying event at small values of the $Z$-boson transverse momentum. The Sherpa event generator shows larger deviations from the measured observables than Pythia8 and Herwig7. Typically, all three Monte Carlo generators provide predictions that are in better agreement with the data at high $Z$-boson transverse momenta than at low $Z$-boson transverse momenta and for the observables that are less sensitive to the number of charged particles in the event.Comment: 36 pages plus author list + cover page (54 pages total), 14 figures, 4 tables, submitted to EPJC, All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2014-0

Transverse-momentum and pseudorapidity distributions of charged hadrons in pp collisions at √s=0.9 and 2.36 TeV

Measurements of inclusive charged-hadron transverse-momentum and pseudorapidity distributions are presented for proton-proton collisions at root s = 0.9 and 2.36 TeV. The data were collected with the CMS detector during the LHC commissioning in December 2009. For non-single-diffractive interactions, the average charged-hadron transverse momentum is measured to be 0.46 +/- 0.01 (stat.) +/- 0.01 (syst.) GeV/c at 0.9 TeV and 0.50 +/- 0.01 (stat.) +/- 0.01 (syst.) GeV/c at 2.36 TeV, for pseudorapidities between -2.4 and +2.4. At these energies, the measured pseudorapidity densities in the central region, dN(ch)/d eta vertical bar(vertical bar eta vertical bar and pp collisions. The results at 2.36 TeV represent the highest-energy measurements at a particle collider to date